Right Triangle Trigonometry

Objectives:Evaluate trigonometric functions of acute anglesUse the fundamental trigonometric identitiesUse trigonometric functions to model and solve real-life problems

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Trigonometric Functions

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Example 1

• Evaluate the six trig functions of the angle shown in the right triangle

• sin =

• cos =

• tan =

• csc =

• sec =

• cot =

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YOU TRY

• Evaluate the six trig functions of the angle shown in the right triangle

• sin =

• cos =

• tan =

• csc =

• sec =

• cot =

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Example 2

Find if

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You Try

Find if

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Example 3• Evaluating the following to the nearest hundredths using a

calculator:

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Example 4• Find the value of x for the right triangle shown

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x

15

30°

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Example 5• Solve ∆ABC (i.e. find the measures of all the unknown angles

and sides of the triangle).

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A

B

C

62°

6c

b

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You Try• Solve ∆ABC.

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A

B

C30°

ac

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Example 6• Find the measure of angle B to the nearest tenth (ONE decimal

place ).• .

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A

B

C

915

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You Try

Find the measure of angle A to the nearest hundredths (TWO decimal places ).

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A

B

C

12

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Example 7• Solve ∆ABC (i.e. find the measures of all the unknown angles

and sides of the triangle).

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A

B

C

9c

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You Try• Solve ∆ABC.

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A

B

C

12

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Victory Lap

Find the unknown value:

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